Correct Option
To determine the car with the maximum average speed, the distance travelled by each car and the time taken must be calculated. The average speed is derived from the formula: Average Speed = Distance / Time.
The total payment for each car is calculated as the sum of the hiring rate per kilometer and the cost of diesel consumed. Let 'D' represent the distance travelled and 'M' denote the mileage (km/l).
Total Payment = (₹ 6/km × D) + (₹ 40/litre × (D/M))
Car A:
- Given: Mileage = 8 km/l, Time = 20 hours, Total Payments = ₹ 2120
- Let the distance travelled be 'a'.
- 2120 = 6a + 40 × (a/8)
- 2120 = 6a + 5a
- 2120 = 11a
- a = 2120 / 11 km
- Average Speed = a / 20 = (2120 / 11) / 20 = 2120 / (11 × 20) ≈ 9.636 km/hr
Incorrect Options
Car B:
- Given: Mileage = 10 km/l, Time = 25 hours, Total Payments = ₹ 1950
- Let the distance travelled be 'b'.
- 1950 = 6b + 40 × (b/10)
- 1950 = 6b + 4b
- 1950 = 10b
- b = 195 km
- Average Speed = b / 25 = 195 / 25 = 7.8 km/hr
Car C:
- Given: Mileage = 9 km/l, Time = 24 hours, Total Payments = ₹ 2064
- Let the distance travelled be 'c'.
- 2064 = 6c + 40 × (c/9)
- 2064 = (54c + 40c) / 9
- 2064 = 94c / 9
- c = (2064 × 9) / 94 ≈ 197.617 km
- Average Speed = c / 24 = (197.617) / 24 ≈ 8.234 km/hr
Car D:
- Given: Mileage = 11 km/l, Time = 22 hours, Total Payments = ₹ 1812
- Let the distance travelled be 'd'.
- 1812 = 6d + 40 × (d/11)
- 1812 = (66d + 40d) / 11
- 1812 = 106d / 11
- d = (1812 × 11) / 106 ≈ 188.037 km
- Average Speed = d / 22 = (188.037) / 22 ≈ 8.547 km/hr
Comparing the calculated average speeds:
- Car A: ≈ 9.636 km/hr
- Car B: 7.8 km/hr
- Car C: ≈ 8.234 km/hr
- Car D: ≈ 8.547 km/hr
Car A maintained the maximum average speed among the four cars.